NTA JEE Mains 29th Jan 2024 Shift 2

A particle is moving in a circle of radius $$50$$ cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $$t = 0$$ is $$4 \text{ m s}^{-1}$$, the time taken to complete the first revolution will be $$\frac{1}{\alpha}\left[1 - e^{-2\pi}\right]$$ s, where $$\alpha =$$ ______.

A body of mass $$5$$ kg moving with a uniform speed $$3\sqrt{2} \text{ m s}^{-1}$$ in $$X-Y$$ plane along the line $$y = x + 4$$. The angular momentum of the particle about the origin will be ______ kg m$$^2$$ s$$^{-1}$$.

Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections are in the ratio $$4 : 1$$ and force $$F_1$$ is applied to $$P$$, an extension of $$\Delta l$$ is produced. The force which is required to produce same extension in $$Q$$ is $$F_2$$. The value of $$\frac{F_1}{F_2}$$ is ______.

A simple harmonic oscillator has an amplitude $$A$$ and time period $$6\pi$$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $$x = A$$ to $$x = \frac{\sqrt{3}}{2}A$$ will be $$\frac{\pi}{x}$$ s, where $$x =$$ ______.

In the given circuit, the current flowing through the resistance $$20 \;\Omega$$ is $$0.3$$ A, while the ammeter reads $$0.9$$ A. The value of $$R_1$$ is ______ $$\Omega$$.

A charge of $$4.0 \;\mu$$C is moving with a velocity of $$4.0 \times 10^6 \text{ m s}^{-1}$$ along the positive $$y$$-axis under a magnetic field $$B$$ of strength $$\left(2\hat{k}\right)$$ T. The force acting on the charge is $$x\hat{i}$$ N. The value of $$x$$ is ______.

A horizontal straight wire $$5$$ m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $$0.60 \times 10^{-4}$$ Wb m$$^{-2}$$. The instantaneous value of emf induced in the wire when its velocity is $$10 \text{ m s}^{-1}$$ is ______ $$\times 10^{-3}$$ V.

In the given figure, the charge stored in $$6\;\mu$$F capacitor, when points $$A$$ and $$B$$ are joined by a connecting wire is ______ $$\mu$$C.

In a single slit diffraction pattern, a light of wavelength $$6000$$ $$\mathring{A}$$ is used. The distance between the first and third minima in the diffraction pattern is found to be $$3$$ mm when the screen is placed $$50$$ cm away from slits. The width of the slit is ______ $$\times 10^{-4}$$ m.

Hydrogen atom is bombarded with electrons accelerated through a potential different of $$V$$, which causes excitation of hydrogen atoms. If the experiment is being formed at $$T = 0$$ K. The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $$\frac{\alpha}{10}$$ V, where $$\alpha =$$ ______.